The Redirections looks interesting, but doesn’t that just write to the htaccess folder anyway?

The Redirection plugin does not seem modify the .htaccess file. I have tried it and the file is the same as before.

I created a redirect from edreach.us/feed/podcast (main podcast feed) feeds.feedburner.com/edreachnetwork
And guess what? It’s updated.

That does not surprise me. It is like it should be. The only thing which sounds a little bit strange is what the Podtrac guy told you about the redirect loop. I guess is that you have registered your feed URL(s) at the Podtrac server, the server retrieves the information in a certain interval from this address and manufactures a new feed (which has a Podtrac URL). But you have created a redirect on your server to this Podtrac URL so that every incomming request gets redirected to the Podtrac URL. What probably happens when you that is, that the Podtrac server tries to update its informations and gets redirected back to itself by your server. The result is: no update. The information that the Podtrac server has is probably from the time before you created the redirection to the Podtrac URL.

One solution to solve this, is to modify your redirects in a way that they only redirect all requests except the ones from the Podtrac Server.
You will probably need a RewriteCond based on the IP (see an example) or the referrer URL (see an exmaple) of the Podtrac server.
For instance if the Podtrac request comes from an address which end with podtrac.com then the condition could look like: